3.24/1.58	YES
3.24/1.59	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.24/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.24/1.59	
3.24/1.59	
3.24/1.59	Termination w.r.t. Q of the given QTRS could be proven:
3.24/1.59	
3.24/1.59	(0) QTRS
3.24/1.59	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.24/1.59	(2) YES
3.24/1.59	
3.24/1.59	
3.24/1.59	----------------------------------------
3.24/1.59	
3.24/1.59	(0)
3.24/1.59	Obligation:
3.24/1.59	Q restricted rewrite system:
3.24/1.59	The TRS R consists of the following rules:
3.24/1.59	
3.24/1.59	   b(a(b(b(b(b(x1)))))) -> a(b(b(b(b(b(a(x1)))))))
3.24/1.59	
3.24/1.59	Q is empty.
3.24/1.59	
3.24/1.59	----------------------------------------
3.24/1.59	
3.24/1.59	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.24/1.59	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.24/1.59	The following rules were used to construct the certificate:
3.24/1.59	
3.24/1.59	   b(a(b(b(b(b(x1)))))) -> a(b(b(b(b(b(a(x1)))))))
3.24/1.59	
3.24/1.59	The certificate found is represented by the following graph.
3.24/1.59	The certificate consists of the following enumerated nodes:
3.24/1.59	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62
3.24/1.59	
3.24/1.59	Node 1 is start node and node 2 is final node.
3.24/1.59	
3.24/1.59	Those nodes are connected through the following edges:
3.24/1.59	
3.24/1.59	* 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 3 to 45 labelled a_1(1)* 4 to 5 labelled b_1(0)* 4 to 33 labelled a_1(1)* 5 to 6 labelled b_1(0)* 5 to 21 labelled a_1(1)* 6 to 7 labelled b_1(0)* 6 to 15 labelled a_1(1)* 7 to 8 labelled b_1(0)* 7 to 9 labelled a_1(1)* 8 to 2 labelled a_1(0)* 9 to 10 labelled b_1(1)* 9 to 57 labelled a_1(2)* 10 to 11 labelled b_1(1)* 10 to 51 labelled a_1(2)* 11 to 12 labelled b_1(1)* 11 to 39 labelled a_1(2)* 12 to 13 labelled b_1(1)* 12 to 27 labelled a_1(2)* 13 to 14 labelled b_1(1)* 13 to 9 labelled a_1(1)* 14 to 2 labelled a_1(1)* 15 to 16 labelled b_1(1)* 16 to 17 labelled b_1(1)* 17 to 18 labelled b_1(1)* 18 to 19 labelled b_1(1)* 19 to 20 labelled b_1(1)* 20 to 13 labelled a_1(1)* 21 to 22 labelled b_1(1)* 22 to 23 labelled b_1(1)* 23 to 24 labelled b_1(1)* 24 to 25 labelled b_1(1)* 25 to 26 labelled b_1(1)* 26 to 19 labelled a_1(1)* 27 to 28 labelled b_1(2)* 28 to 29 labelled b_1(2)* 29 to 30 labelled b_1(2)* 30 to 31 labelled b_1(2)* 31 to 32 labelled b_1(2)* 32 to 13 labelled a_1(2)* 33 to 34 labelled b_1(1)* 34 to 35 labelled b_1(1)* 35 to 36 labelled b_1(1)* 36 to 37 labelled b_1(1)* 37 to 38 labelled b_1(1)* 38 to 25 labelled a_1(1)* 39 to 40 labelled b_1(2)* 40 to 41 labelled b_1(2)* 41 to 42 labelled b_1(2)* 42 to 43 labelled b_1(2)* 43 to 44 labelled b_1(2)* 44 to 31 labelled a_1(2)* 45 to 46 labelled b_1(1)* 46 to 47 labelled b_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled b_1(1)* 49 to 50 labelled b_1(1)* 50 to 37 labelled a_1(1)* 51 to 52 labelled b_1(2)* 52 to 53 labelled b_1(2)* 53 to 54 labelled b_1(2)* 54 to 55 labelled b_1(2)* 55 to 56 labelled b_1(2)* 56 to 43 labelled a_1(2)* 57 to 58 labelled b_1(2)* 58 to 59 labelled b_1(2)* 59 to 60 labelled b_1(2)* 60 to 61 labelled b_1(2)* 61 to 62 labelled b_1(2)* 62 to 55 labelled a_1(2)
3.24/1.59	
3.24/1.59	
3.24/1.59	----------------------------------------
3.24/1.59	
3.24/1.59	(2)
3.24/1.59	YES
3.57/1.63	EOF